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WASHINGTON (CBSNewYork/AP) – A deal on Capitol Hill to avert the so-called fiscal cliff was proving elusive Sunday, as a deadline to avert tax hikes on virtually every American worker and block sweeping spending cuts set to strike the Pentagon and other federal agencies grew perilously near.

“There is still significant distance between the two sides, but negotiations continue,” said Senate Majority Leader Harry Reid, D-Nev.

Reid and Senate Republican leader Mitch McConnell remained at odds on such key issues as the income threshold for higher tax rates and how to deal with inheritance taxes, among other issues. McConnell complained that Reid had yet to respond to a GOP offer made Saturday evening and reached out to Vice President Joe Biden, a longtime friend, in hopes of breaking the impasse.

“I want everyone to know I am willing to get this done,” McConnell said. “But I need a dance partner.”

Biden has assumed the lead role for Democrats, and a McConnell spokesman said the Kentucky Republican and the vice president are expected to negotiate by telephone into the night.

“I think we all know we are running out of time,” McConnell said. “There is far too much at stake for political gamesmanship.”

Rank-and-file lawmakers left the Capitol Sunday night with hopes that their leaders would give them something to vote on when they returned Monday morning.

One sign of progress came as Republicans withdrew a long-discussed proposal to slow future cost-of-living increases for Social Security recipients as part of a compromise to avoid the cliff. Democrats said earlier Sunday that proposal had put a damper on the talks, and Republican senators emerging from a closed-door GOP meeting said it is no longer part of the equation.

“I was really gratified to hear that Republicans have taken their demand for Social Security benefit cuts off the table. The truth is they should never have been on the table to begin with,” Reid said late Sunday afternoon. “There is still significant distance between the two sides, but negotiations continue.”

At stake are sweeping tax hikes and across-the-board spending cuts set to take effect at the turn of the year. Taken together, they’ve been dubbed the fiscal cliff, and economists warn the one-two punch _ which leaders in both parties have said they want to avoid _ could send the still-fragile economy back into recession. Tax cuts enacted in 2001 and 2003 expire at midnight Monday, and $109 billion in across-the-board cuts in federal spending this year would also begin this week.

Sen. Dick Durbin, D-Ill., said the two sides remained at odds over the income threshold for higher tax rates and tax levels on large estates. Republicans said that Democratic demands for new money to prevent a cut in Medicare payments to doctors and renew jobless benefits for the long-term unemployed should be financed with cuts elsewhere in the budget. Republicans also balked at a Democratic proposal to use new tax revenues to shut off the across-the-board spending cuts, known as a sequester in Washington-speak.

“Over the next 48 hours, my hope is that people recognize that regardless of partisan differences, our top priority has to be to make sure that taxes on middle class families do not go up, that it would hurt our economy badly,” Obama said on NBC’s “Meet The Press.”

The president also took the chance to rap Republicans for failing to compromise.

“If people start seeing that on Jan. 1 this problem still hasn’t been solved, that we haven’t seen the kind of deficit reduction that we could’ve had had the Republicans been willing to take the deal that I gave them. If they say that people’s taxes have gone up, which means consumer spending is going to be depressed, then obviously that’s going to have an adverse reaction in the markets,” the president warned. “I think anybody objectively who’s looked at this would say that we have put forward not only a sensible deal but one that has the support of the majority of the American people including close to half of Republicans.”

“We don’t yet see an agreement and now the pressure is on Congress to produce,” President Obama said NBC’s “Meet The Press” on Sunday.

Gone, however, is the talk of a grand deal that would tackle broad spending and revenue demands and set the nation on a course to lower deficits. Obama and Republican House Speaker John Boehner were once a couple hundred billion dollars apart of a deal that would have reduced the deficit by more than $2 trillion over ten years.

Republicans have complained that Obama has demanded too much in tax revenue and hasn’t proposed sufficient cuts or savings in the nation’s massive health care programs.

“Our choice is simple – avoid the fiscal cliff and people’s taxes going up or do nothing and let it happen. We didn’t want to be in that position but Speaker Boehner pulled out of the deal a week and a half ago. It’s not fair to blame the president,” said Sen. Charles Schumer, on ABC’s “This Week.”

Obama upped the pressure on Republicans to negotiate a fiscal deal, arguing that GOP leaders have rejected his past attempts to strike a bigger and more comprehensive bargain.

“The offers that I’ve made to them have been so fair that a lot of Democrats get mad at me,” Obama said.

South Carolina Republican Sen. Lindsey Graham is predicting that without at least 28 of the 47 GOP senators on board with any given proposal, House Speaker John Boehner wouldn’t be able to get the votes to pass it.

If McConnell “can’t get 60 percent of us to vote for this deal, it will be hard for Boehner to get it through the House. And I want to vote for it even though I won’t like it because the country’s got a lot at stake here,” Graham said on “Fox News Sunday”.

Sen. Dianne Feinstein, D-Calif., said the 2.1 million Americans whose extended unemployment benefits ran out on Saturday are already feeling the pain of Congress’ inaction.

“From this point on, it’s lose-lose. My big worry is a contraction of the economy, the loss of jobs, which could be well over 2 million in addition to the people already on unemployment. I think contraction of the economy would be just terrible for this nation. I think we need a deal, we should do a deal,” Feinstein said on “Fox News Sunday.”

If a deal is not reached, Obama wants the Democratic-controlled Senate to introduce legislation to keep tax cuts for couples earning up to $250,000 a year, and to keep unemployment benefits.

(TM and Copyright 2012 CBS Radio Inc. and its relevant subsidiaries. CBS RADIO and EYE Logo TM and Copyright 2012 CBS Broadcasting Inc. Used under license. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.)